Telescopers for differential forms with one parameter

• Shaoshi Chen ^[1] ; Ruyong Feng ^[1] ; Ziming Li ^[1] ; Michael F Singer ^[2] ; Stephen M. Watt ^[3]
  1. [1] University of Chinese Academy of Sciences

     University of Chinese Academy of Sciences

     China

     
  2. [2] North Carolina State University

     North Carolina State University

     Township of Raleigh, Estados Unidos

     
  3. [3] University of Waterloo

     University of Waterloo

     Canadá

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-23
• Idioma: inglés
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• Resumen

  • Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given.